Abstract
In this work the two dimensional flow and heat transfer of a Visco-elastic fluid flowing steadily between two walls having periodic deformation and situated symmetrically about a mid plane is studied. The equation of motion and energy are solved with the help of the perturbation method taking the deformation of the boundaries small. Energy equation is solved under two types of thermal boundary conditions; (i) both walls are maintained at the same constant temperature and (ii) one wall is at constant temperature while the other wall is thermally insulated. The effects of visco-elastic parameter ‘K’ on the velocity distribution has been studied by draining the streamlines. We also note that the temperature distribution is not affected the presence of viscoelasticity of the liquid.
Similar content being viewed by others
Data availability
Enquiries about data availability should be directed to the authors.
References
Citron, J.S.: Slow viscous flow between rotating concentric cylinders with axial roughness. ASME J. App. Mech. 29, 188–192 (1962)
Beard, D.W., Walter, K.: Two dimensional flows near a stagnation point. Proc. Camb. Phil. Soc. Camb. Phil. Soc. 60, 667–674 (1964)
Yhan, S.W., Foundation of fluid mechanics, PHI, (1965) pp. 259
Burns, J.C., Parks, T.: Peristaltic motion. J. Fluid Mech. 29, 731–743 (1967)
Goldstein, J.L., Sparrow, E.M.: Heat/mass transfer characteristic for flow in a corrugated wall channel. ASME J. Heat Mass Transf. 38, 3219–3230 (1977)
Biswal, T.: Flow and heat transfer of a visco-elarstic liquid between two wavy walls. Rev. Roum. Phys Tome 28(9), 754–772 (1983)
Wang, G., Vanka, S.P.: Convective heat transfer in periodic wavy passages. Int. J. Heat Mass Transfer 19, 39–48 (1995)
Blancher, S., Creff, R., Quere, P.L.: Effects of tollmien Schlichting on convective heat transfer in a wavy channel. Int. J. Heat Fluid Flow 19, 39–48 (1998)
Wirtz, R.A., Huang, F., Greiner, M.: Correlation of fully developed heat transfer and pressure drop in a symmetrically grooved channel. ASME. J. Heat Transfer 121, 236–239 (1999)
Malasetty, M.S., Umavathi, J.C., Pratap Kumar, J.: Convective flow and heat transfer in a composite porous medium. J. Porous media 4, 15–22 (2001)
Chen, C.K., Wang, C.C.: Heat transfer characteristics of wavy-walls channels in micropolar fluids. Tsinghua Sc. Tech. 7(2), 146–154 (2002)
Jang, J.H., Yan, W.M.: Mixed convection heat and mass transfer along a vertical wavy surface. Int. J. Heat Mass Transfer 47, 419–428 (2004)
Yao, L.S.: Natural convection along a vertical complex wavy surface. Int. J. Heat Mass Transfer 49, 281–286 (2006)
Malasetty, M.S., Umavathi, J.C., Pratap Kumar, J.: Magneto convection of two immiscible fluids in a vertical enclose. Heat Mass Transfer 42, 977–993 (2006)
Umavathi, J.C., Mateen, A., Chamkha, A.J., Al-Mudhaf, A.: Oscillatory Hartman two fluid flow and heat transfer in a horizontal channel. Int. J. Appl. Mech. Engg. 11, 155–178 (2006)
Umavathi, J.C., Manjula, M.H., Pop, I., Liu, I.C.: Flow and heat transfer of couple stress and viscous fluid in a vertical channel. Int J. Appl. Mech. Engg. 12, 537–555 (2007)
Umavathi, J.C., Liu, I.C.S., Meera: Unsteady flow and heat transfer of three immiscible fluids. Int. J. Appl. Mech. Engg. 13, 1079–1100 (2008)
Umavathi, J.C., Pratap Kumar, J., Shekar, M.: Mixed convective flow of immiscible viscous fluids confined between a long vertical wavy wall and a parallel flat wall. Int. J. Engg. Sci. Tech. 2(6), 256–272 (2010)
Prathap, K.J., Umavati, J.C.: The effect of electromagnetic field on free convective heat transfer in a vertical wavy channel divided by a perfectly conductive Baffle. J. Heat Mass Momentum Transfer 1(2), 47–73 (2013)
Birader, M.: Magneto-convective flow and heat transfer of two immiscible fluids between vertical wavy wall and parallel flat wall. IJRET 3(3), 777–790 (2014)
Umavathi, J.C., Shekar, M.: Mixed convective flow of immiscible fluids in a vertical corrugated channel with traveling thermal waves. J. King Suad Unvi. Engg. Sci. 26, 49–68 (2014)
Josephat, N.O., Sigey, J.K., Okelo, J.A., Okwoyo, J.M.: Effect of electromagnetic field on forced convective heat transfer in open ended vertical wavy channel divided by a perfectly conductive Baffle. SIJ 3(3), 38–43 (2015)
Amini, M., Najafi, M., Dorosti, Q., Biglarian, H., Ghasemi, E.: Effects of waviness and temperature variation on the fluid flow and natural convection in an inclined corrugated channel. IJAMR 4(1), 163–176 (2015)
Venkataswarlu, B., Bhagya Lakshmi, K., Samantha Kumari, K., Satya Narayan, P.V.: Magnetohydrodynamic oscillatory flow of a physiological fluid in an irregular channel. Springer Nature Appl. Sci. 1, 1223 (2019)
Funding
The authors have not disclosed any funding.
Author information
Authors and Affiliations
Contributions
I have reviewed the manuscript
Corresponding author
Ethics declarations
Conflict of interest
The authors have not disclosed any competing interests.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Sahoo, A.C. An Analytical Study of the Flow and Heat Transfer of Viscoelastic Fluid Between Two Wavy Walls Situated Symmetrically About a Mid Plane. Int. J. Appl. Comput. Math 10, 77 (2024). https://doi.org/10.1007/s40819-024-01719-3
Accepted:
Published:
DOI: https://doi.org/10.1007/s40819-024-01719-3